.... But if you truly want the benefits of study, or meditation, or exercise, or anything else, I have to believe that the best way to get them is to buckle down at the thing itself, not at some more engaging, less demanding activity that you hope will bring you the gain without the pain.

Granted. I agree that what passes for a study or meditative environment is often inappropriate to the stated goals and objectives of the true task at hand. Agreement is good.
On the other hand: ever tried studying while standing in a crowded subway car at rush hour while the train shakes and rattles around a curve at 50mph making the wheels screech at 120db? It's done all the time. So is meditation. So is Aikido. It's very much at the heart of why OSensei developed Aikido. And is also why Matthew has kindly supplied us with more information about Music and Learning which I just noticed while keyboarding this. That's all the time I have for now, I have a bunch of Aiki gardening to do.

Maybe what I just wrote doesn't help explain why it's reasonable to believe an integration of Music and Aikido can be of great value in the real world. So, here's a link sent to me by a Sensei who knows more about these things than I ever will. He calls it Aiki Music.